How do you simplify #sin(sin^-1( 3/5) + tan^-1( 7/24))#?

1 Answer
P dilip_k
Apr 16, 2016

#=4/5#

Explanation:

#=sin(sin^-!(3/5)+cot^-1(24/7))#
#=sin(sin^-!(3/5)+csc^-1sqrt(1+(24/7)^2))#
#=sin(sin^-!(3/5)+csc^-1(25/7))#
#=sin(sin^-!(3/5)+sin^-1(7/25))#

#=sinsin^-!(3/5)cossin^-1(7/25)+cossin^-!(3/5)sin sin^-1(7/25))#
#=(3/5)coscos^-1sqrt(1-(7/25)^2)+cosscos^-1sqrt(1-(3/5)^2)sin sin^-1(7/25)#
#=3/5xx24/25+4/5xx7/25=100/125=4/5#

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